Determining parameters in generalized thermomechanics for metamaterials by means of asymptotic homogenization

TL;DR

This paper develops a computational approach using asymptotic homogenization and FEM to determine parameters in generalized thermomechanics models for metamaterials with complex microstructures.

Contribution

It introduces a method to numerically compute all parameters in generalized thermomechanics models based on microstructure using asymptotic homogenization.

Findings

Validated method with symmetric and random void distributions

Identified length-scale where generalized thermoelasticity is necessary

Demonstrated use of open-source FEM tools for parameter calculation

Abstract

Advancement in manufacturing methods enable designing so called metamaterials with a tailor-made microstructure. Microstructure affects materials response within a length-scale, where we model this behavior by using the generalized thermomechanics. Strain gradient theory is employed as a higher-order theory with thermodynamics modeled as a first-order theory. Developing multiphysics models for heterogeneous materials is indeed a challenge and even this ``simplest'' model in generalized thermomechanics causes dozens of parameters to be determined. We develop a computational model by using a given microstructure, modeled as a periodic domain, and numerically calculate all parameters by means of asymptotic homogenization. Finite element method (FEM) is employed with the aid of open-source codes (FEniCS). Some example with symmetric and random distribution of voids in a model problem verifies the method and provides an example at which length-scale we need to consider generalized thermoeleasticity in composite materials.